Identification and digital control of a household refrigeration system with a variable speed compressor

• ARMAX model for a household refrigerator that uses a variable speed compressor.
• A digital PI controller was designed to control the compartment air temperature.
• Simulations were run on the closed-loop system, obtaining satisfactory results.
• Digital PI controller can control the refrigerator in its entire operation range.
• Refrigerator with variable speed compressor consumes 15% less power.

This paper presents an autoregressive–moving-average model with exogenous inputs (ARMAX model) and a digital controller for a household refrigeration system that uses a variable speed compressor. The ARMAX model takes as inputs the RPM of the compressor and environmental variables, such as temperature and relative humidity. Additionally, the output variables were defined as the temperatures of the freezer, the evaporator plate, and the compartment air and the compartment air relative humidity. The results of the experimental tests showed that the ARMAX model reproduces with high accuracy the dynamic behavior of the refrigeration system with less than 7% error. Tests of energy consumption and food storage were performed according to the NTC 2078 standard, which applies to household refrigeration systems manufactured or sold in Colombia. These tests indicated that the refrigeration system with a variable speed compressor consumes 15% less energy than an equivalent conventional refrigeration system and that the temperature profiles inside the compartment are more stable.